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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.19502 |
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| _version_ | 1866909213178986496 |
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| author | Grats, Yuri V. Spirin, Pavel |
| author_facet | Grats, Yuri V. Spirin, Pavel |
| contents | We develop precise formulation for the effects of vacuum polarization near a pointlike source with a zero-range ($δ$-like) potential in three spatial dimensions.
There are different ways of introducing $δ$-interaction in the framework of quantum theory. We discuss the approach based on the concept of self-adjoint extensions of densely defined symmetric operators. Within this approach we consider the real massive scalar field in three-dimensional Euclidean space with a single extracted point. Appropriate boundary conditions imposed at this point enable one to consider all self-adjoint extensions of $- Δ$ as operators which can describe a pointlike source with a zero-range potential. In this framework we compute the renormalized vacuum expectation value of the field square $\langle ϕ^{ 2}(x)\rangle_{\rm ren}$ and the renormalized vacuum average of the scalar-field's energy-momentum tensor $\langle T_{μν}(x)\rangle_{\rm ren}$. Asymptotic cases are discussed in detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vacuum Polarization Effects of Pointlike Impurity Grats, Yuri V. Spirin, Pavel High Energy Physics - Theory We develop precise formulation for the effects of vacuum polarization near a pointlike source with a zero-range ($δ$-like) potential in three spatial dimensions. There are different ways of introducing $δ$-interaction in the framework of quantum theory. We discuss the approach based on the concept of self-adjoint extensions of densely defined symmetric operators. Within this approach we consider the real massive scalar field in three-dimensional Euclidean space with a single extracted point. Appropriate boundary conditions imposed at this point enable one to consider all self-adjoint extensions of $- Δ$ as operators which can describe a pointlike source with a zero-range potential. In this framework we compute the renormalized vacuum expectation value of the field square $\langle ϕ^{ 2}(x)\rangle_{\rm ren}$ and the renormalized vacuum average of the scalar-field's energy-momentum tensor $\langle T_{μν}(x)\rangle_{\rm ren}$. Asymptotic cases are discussed in detail. |
| title | Vacuum Polarization Effects of Pointlike Impurity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.19502 |